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1613
Why the Atlantic cod (Gadus morhua) stock off
eastern Nova Scotia has not recovered
Caihong Fu, Robert Mohn, and L. Paul Fanning
Abstract: An age-structured population dynamics model, incorporating interactions between Atlantic cod (Gadus
morhua), the fishery, and the grey seal (Halichoerus grypus) population, was applied to the cod stock off eastern Nova
Scotia (Northwest Atlantic Fisheries Organization Divisions 4Vs and 4W, commonly abbreviated to 4VsW), a stock
that has dramatically declined since the late 1980s. Mortality was modeled as having three components: fishing mortality (F), seal predation (Mp), and all other sources of natural mortality (M). Specifically, M was assumed to be distinct
for immature cod (ages 1–4; M i) and mature cod (age 5 and older; Mm), and respective annual variations were estimated. Parameters estimated also included recruitment (cod abundance at age 1; R), F, and Mp. Based on our estimates
of F, Mp, and M, it is unlikely that the collapse of the 4VsW cod stock can be attributed to a sudden increase in M;
fishing appears to have been the primary cause for the stock’s decline. However, after the moratorium on commercial
fishing in 1993, increasing Mp and Mm and low R may have contributed to the failure of the 4VsW cod stock to recover.
Résumé : Un modèle de dynamique de population basé sur les structures d’âges qui incorpore les interactions entre la
Morue franche (Gadus morhua), les pêches commerciales et la population de Phoques gris (Halichoerus grypus) a été
appliqué au stock de morues du large de la côte est de la Nouvelle-Écosse (divisions 4VsW de l’Organisation des pêches de l’Atlantique nord-ouest), un stock qui a chuté de façon dramatique depuis la fin des années 1980. La modélisation de la mortalité a trois composantes, la mortalité due à la pêche (F), la prédation par les phoques (Mp) et les autres
sources de mortalité naturelle (M). Plus précisément, une mortalité distincte est attribuée aux morues immatures (âges
1–4, M i) et matures (âges 5 et plus, Mm) et, pour chacune, les variations annuelles sont estimées. Les variables,
comme le recrutement (R, abondance des morues à l’âge 1), F et Mp, sont aussi estimées. D’après nos estimations de
F, Mp et M, il est peu probable que le déclin du stock 4VsW soit attribuable à une augmentation soudaine de M; les
pêches commerciales semblent avoir été la cause principale de la chute du stock. Toutefois, après le moratoire sur les
pêches commerciales en 1993, des valeurs croissantes de Mp et de Mm et un R faible peuvent avoir contribué à
l’incapacité du stock 4VsW de se rétablir.
[Traduit par la Rédaction]
Fu et al.
1623
Introduction
Six Canadian stocks of Atlantic cod (Gadus morhua)
ranging from southern Labrador to the continental shelf off
eastern Nova Scotia collapsed almost simultaneously to the
point where moratoria on commercial exploitation were declared in 1992 and 1993 (Myers et al. 1996). The reasons for
these collapses were unknown, and were the subject of considerable debate. Some linked stock declines to natural
causes and others to fishing activities. The ongoing debate
over many other collapsed species across many jurisdictions
underscores the difficulties of unambiguously demonstrating
the relative influences of environmental, ecosystem, and
Received August 2, 2000. Accepted May 9, 2001. Published
on the NRC Research Press Web site at http://cjfas.nrc.ca on
July 18, 2001.
J15896
C. Fu,1,2 R. Mohn, and L.P. Fanning. Department of
Fisheries and Oceans, Bedford Institute of Oceanography,
Marine Fish Division, P.O. Box 1006, Dartmouth,
NS B2Y 4A2, Canada.
1
2
Corresponding author (e-mail: [email protected]).
Present address: Department of Fisheries and Oceans, Pacific
Biological Station, Nanaimo, BC V9R 5K6.
Can. J. Fish. Aquat. Sci. 58: 1613–1623 (2001)
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fishing effects on heavily exploited species (Frank et al.
1996).
For the six cod stocks off eastern Canada, recruitment of
year-classes that should have contributed most to the spawning stock at the time of collapses was found not to differ
from recruitment levels in earlier years (Myers et al. 1997).
High fishing mortality was identified as the primary cause
for these collapses (Hutchings and Myers 1994; Myers and
Cadigan 1995; Myers et al. 1996). On the other hand, Rose
et al. (2000) argues that the collapses cannot be attributed in
total to fisheries. Major environmental changes took place
during the period of cod decline (Drinkwater and Mountain
1997), which may have led to the shift of cod distribution
(Rose et al. 2000), reduced recruitment (deYoung and Rose
1993), and increased vulnerability to overfishing (Rose and
Kulka 1999).
It was also suggested that body condition factors for cod
in the northern Gulf of St. Lawrence declined throughout the
early 1990s (Lambert and Dutil 1997), owing to poor environmental conditions (Dutil et al. 1999). The reduced condition of cod may have led to an increase in natural mortality,
particularly for adults that have to invest energy reserves in
reproduction (Lambert and Dutil 2000; Dutil and Lambert
2000). Diagnostic analysis of commercial catch and researchsurvey data obtained from the cod stock off southern
DOI: 10.1139/cjfas-58-8-1613
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1614
Labrador and eastern Newfoundland suggested that large
amounts of the 1987 year-class died as 4-year-olds in 1991
and as 5-year-olds in 1992 (Shelton and Lilly 2000). Although Myers and Cadigan (1995) rejected the hypothesis
for the same cod stock that natural mortality increased in
1991, the increasing divergence of recruitment between
research-survey analysis and virtual population analysis suggested increased losses of fish (Myers et al. 1997). Myers et
al. (1997) attributed the losses to increased misreporting and
discarding of catches of young. However, the quantity of
missing fish in relation to the capacity of fishery at that time
suggested that additional factors such as an increase in natural mortality due to reduced condition also played a role
(Shelton and Lilly 2000). In addition, increased predation by
seals may also have contributed to the collapse (Mohn and
Bowen 1996).
In the case of each of the six collapsed cod stocks off
eastern Canada, we may never be able to determine the relative importance of environmental changes (including predation) and fishing activities in the population changes.
Nevertheless, there is little doubt that the sequential population analysis (SPA) which failed to provide acceptable population reconstruction during the time of population decline
(Mohn 1999; Shelton and Lilly 2000) must have violated
one or more of the model assumptions, such as constant
natural mortality, accurate catch data, or constant researchsurvey catchability (Shelton and Lilly 2000). Thus, the most
important question in stock assessment and fisheries management at this point is how to develop more realistic population models that require fewer and less rigid assumptions.
This paper presents a modelling exercise intended to shed
light on what may have happened to the cod stock off eastern Nova Scotia in Northwest Atlantic Fisheries Organization Divisions 4Vs and 4W (Fig. 1), commonly abbreviated
to 4VsW.
The cod stock in 4VsW has been managed as one unit, although there is evidence that the cod stock in 4VsW comprises separate substocks (reviewed in Halliday and Pinhorn
1990). Before 1993, the stock was an important commercial
resource. Catches averaged 49 600 (ranging from 10 000 to
80 000) metric tonnes (t) annually (Mohn et al. 1998). In
1992, the total catch reached 29 805 t under a total allowable
catch (TAC) of 35 200 t. In 1993, the TAC was reduced to
11 000 t, in part because of the shortfall in 1992. Landings
in 1993 amounted to 3474 t (Mohn et al. 1998), again considerably lower than the TAC. Population abundance of
4VsW cod appeared to have declined rapidly during 1993.
The directed fishery for 4VsW cod was closed in September
1993, and abundance not only has remained low but has
continued to decline since then.
Stock assessments of 4VsW cod have been undertaken
routinely since 1975 (Halliday 1975). Stock assessments
made before 1997 were based on SPA, assuming constant
natural mortality of 0.2 over age and time (Fanning et al.
1996). However, there were concerns about the retrospective
pattern in parameter estimates of population biomass and
fishing mortality, i.e., the estimates deviated systematically
as data were annually eliminated from or added to the assessment (Mohn 1999). Owing to the strong retrospective
pattern, the most recent assessment was revised by assuming
that natural mortality increased from 0.2 to 0.4 after 1985. In
Can. J. Fish. Aquat. Sci. Vol. 58, 2001
addition, predation by grey seals (Halichoerus grypus) was
explicitly incorporated into the model because of increasing
concern about removals attributed to seals (Mohn et al. 1998).
These adjustments resulted in the retrospective pattern being
greatly reduced, but its causes for the most part remained
unknown. Also unresolved was what caused the population
to decline, and whether consumption by seals had played an
important role in cod population dynamics.
This paper develops a model based on a framework of interactions between cod, fisheries, and seals in which annual
variations in natural mortality for both immature (ages 1–4)
and mature cod (age 5 and older) were estimated explicitly.
In addition, more parameter uncertainties were incorporated,
including those in gear selectivity. The goal of this paper is
to use this model to estimate time-varying mortality parameters and recruitment, to give a better rationale for the decline
of the 4VsW cod stock and especially its failure to recover.
Methods
Data
Data used in the present work include catch at age from com~
mercial fishery (C t, a ), exploitable number at age estimated from
~
July research surveys (N t, a ), number at age consumed by grey seals
~p
(C t, a ) estimated according to Mohn and Bowen (1996), and cod
weight at age estimated from commercial-fishery samples (Wa). Index t is for the years 1970–1997 and index a for ages from 1 to
maximum age, A. The maximum age, A, was set at 12 to avoid
many zeros in the data. There are two sets of estimated seal~
consumption data, C tp, a , depending on the assumption of cod fraction in the diet of grey seals (Mohn and Bowen 1996). When the
cod fraction in the seal diet is assumed to be constant, calculation
~
of C tp, a is independent of the size of the cod stock. If cod fraction is
assumed to be proportional to cod-stock size, then the calculation
~
of C tp, a needs to be updated when the cod-stock size changes.
Population model
An age-structured separable model was constructed for the 4VsW
cod stock. Because it is more convenient and easier to estimate a
time series of parameters by estimating their deviations from a
mean value (Otter Research Ltd. 1998), annual recruitment (R) at
age 1 was modeled as ln(Rt) = ln(R) + hRt , where R is the assumed
average level set at 12 million and hRt is the deviation term. Similarly, instantaneous fishing mortality (F) of fully selected cod was
modeled as ln(Ft) = ln (F ) + h Ft with F being set at 0.4. Cod ageclasses were separated into two groups according to their maturity,
following Mohn et al. (1998), where it was assumed that immature
cod were aged 1–4 and mature cod were aged 5 and older. Natural
mortality (M) was assumed to be distinct for immature cod (Mi)
and mature cod (Mm). Mortalities Mi and Mm and predation mortality (Mp) were modeled as the time-series structure of a random walk: ln(M ti+ 1 ) = ln(M ti ) + hit , ln(M tm+ 1 ) = ln(M tm ) + hm
t , and
ln(M tp+ 1 ) = ln(M tp ) + h pt where hit , hmt , and h pt are the deviation
terms.
Selectivity for the research-survey gear at age a was modeled as
1
s
a logistic curve s as =
s
s . Parameters g , the shape param1 + e -g (a - d )
eter, and d s , the age at which 50% of the individuals are vulnerable
to research-survey gear, were assumed to be time-independent.
Gear selectivity for commercial fishing was modeled as three distinct logistic curves based on changes in the regulated trawl gear
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Fu et al.
1615
Fig. 1. Map showing the location of Northwest Atlantic Fisheries Organization Divisions 4VsW off eastern Nova Scotia, Canada.
mesh size over the fishing history: s aC k =
1
Ck
Ck
e -g (a - d )
, with
1+
k = 1 for the period 1970–1976, k = 2 for 1977–1982, and k = 3 for
1983–1997. Predation selectivity was modeled as a descending lo1
for ages 2–7. With age 1 cod, selecgistic curve: s ap =
p
p
1 + e g (a - d )
tivity, s1p , was estimated individually to eliminate the pattern of
consistently positive residuals of numbers of age 1 cod consumed.
Predation selection, s ap , is assumed to be 0.0 for age 8 and older,
based on seal-diet data.
The expected number of age 1 cod in year 1970 was calculated
hR
hR
as N1970 , a = Re 1970 . For ages above 1, N1970,a = Re 1970 - a + 1
e -M .
Õ
a
Natural mortality during the initial period of A – 1 years before
1970, M , was assumed to be constant at 0.2 because it has little effect on the estimation of other parameters (Fu and Quinn 2000).
Expected numbers at age a in subsequent years are
Nt,a = Nt–1,a–1e
- Z t - 1, a - 1
, 1 < a < A – 1,
and
N t, A+ = Nt–1,A–1e
- Z t - 1, A - 1
+ Nt–1,Ae
- Z t - 1, A
Total mortality is Zt, a = Ft s aC k + M ti + M tp s ap , a = 1, . . ., 4, for immature cod and Zt, a = Ft s aC k + M tm + M tp s ap , a = 5, . . ., A for mature cod.
Expected numbers of catch at age follow the Baranov catch
F s Ck
equation (Quinn and Deriso 1999): C t, a = N t, a t a (1 - e -Z t , a ).
Zt, a
Because of a change in research-vessel trawl gear in 1982 from
Yankee 36 with width × vertical headline 11.0 × 3.4 m2 to Western
IIA with 12.5 × 4.6 m2, survey catchability (q) was assumed to be
different for the two periods. Thus, the expected numbers at age a
for research surveys were calculated as N ts, a = q j N t, a s as , where j = 1
for the period 1970–1981 and j = 2 for 1982–1997. Catchabilities
q1 and q2 were arbitrarily set at 0.4 and 0.6, resepectively, the ratio
of which is approximately the difference in net openings. Other
levels were tried for evaluating sensitivity to their changes. Expected numbers of consumption at age a by grey seals in year t is
C tp, a = N t, a
M tp sap
(1 - e- Z t , a )
Z t, a
Parameters estimated include the time-dependent deviation terms
hRt , htF , htp , hit , and hm . In addition, the following selectivity parameters for research survey, commercial fishing, and predation
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1616
Can. J. Fish. Aquat. Sci. Vol. 58, 2001
Fig. 2. Parameter estimates obtained using consumption data of
constant cod fraction in seal diet under three assumptions of
catchability (q): q1 (before 1982) and q2 (1982 and afterwards)
are set at 0.4 and 0.6 (line without symbols), both at 0.3 (line
with solid squares), and 0.8 (line with solid triangles), respectively. The estimates include predation mortality averaged over
ages 1–4, Mp (a), natural mortality of immature cod, Mi (b),
natural mortality of mature cod, Mm (c), instantaneous fishing
mortality of fully recruited fish, F (d), recruitment, R (e), and
spawning-stock biomass, SSB (f).
were estimated: g s , d s , g C k , d C k , s 1p , g p , and d p . Parameter estimation was accomplished using the software AD Model Builder,
which estimates parameters in a step-by-step fashion known as a
multiphase procedure (Otter Research Ltd. 1998). A nonlinear
least-squares (NLS) parameter-estimation procedure was applied.
The NLS is robust to error structure in the data, such as in
multinomial catch-at-age data, and could be expected to find parameter estimates more rapidly than the multinomial maximum
likelihood method (Kimura 1990). Square-root transformation following Quinn et al. (1998) was used for all data. A logarithmic
transformation was also applied and yielded quantitatively similar
results, which are not presented. The following objective function
is minimized for estimating parameters:
f = lC
å å çæè
t
2
~
C t, a - C t, a ÷ö
ø
a
2
~
+ l N s å å æçè N t, a - N ts, a ö÷ø
t
a
~
+ l C p å å æç C t,pa - C tp, a ö÷
è
ø
t
2
a
2
M 2
+ l M i å (hM
t ) + l M m å (ht )
i
m
t
Weighting factors l C , l N s , and l C p were determined on the basis
of the inverse of their residual variances and were set at 1.0, 0.3,
and 1.0, respectively. In trials, parameter estimation was little affected by weighting factors of different data sources, which is coni
sistent with the mconclusion in Fu (2000). The terms l M i
(hMt )2
M 2
and l M m
(h t ) are penalties controlling the degree of variability in the time series of Mi and Mm estimates from year to year.
~
The values of l M i and l M m are calculated as the product of N t, a re~
sidual variance, l N s , an assumed coefficient of variation of N t, a
i
m
(Fu and Quinn 2000), and the relative variation of M and M . We
assigned 7500.0 and 5000.0 to l M i and l M m , respectively. The
sensitivity of parameter estimation to the choice of l M i and l M m
levels was examined.
å
å
Standard error and retrospective analysis
The bootstrap method (Efron and Tibshirani 1993) was used to
estimate standard errors for the parameter estimates and predicted
spawning stock biomass (SSB). Residuals from the original model
were resampled. Parameter estimation was repeated 500 times
using bootstrap data. Retrospective analysis (Mohn 1999) was conducted to evaluate the ability of the model to estimate parameters
for the terminal years. This was done by reestimating parameters
after leaving out successive terminal data with the full series,
1970–1997, which was eventually reduced to 1970–1983.
Results
Sensitivity to catchability
~
Survey data, N t, a , are calibrated to the estimated population number at age using the catchability from research sur© 2001 NRC Canada
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Fu et al.
veys. Fu (2000) demonstrates that q cannot be estimated
with sufficient accuracy simultaneously with natural mortality (M), and it is better to keep q at a given level while estimating M each year even when there is variation in q (Fu
and Quinn 2000). To examine how q affects the estimation
of population parameters, we adopted various time-invariant
levels of q and compared the parameter estimates and residual sum of squares (RSS). For purposes of the sensitivity
evaluation, a constant fraction of cod in the seal diet is
~
assumed to eliminate the nuisance effect of different C tp, a
values corresponding to different levels of q. In addition to
the initially set q1 and q2 values of 0.4 and 0.6, alternative
levels of 0.3 and 0.8 are also tried.
The estimation of Mp (shown as the average over ages 1–
4), Mi, and R is robust to the assumed levels of q (Fig. 2).
However, the estimated Mm, F, and SSB change dramatically
in magnitude, with Mm and SSB decreasing and F increasing, when q increases from 0.3 to 0.8. The parameter estimates with q1 and q2 values of 0.4 and 0.6 are in between,
and RSS is the lowest (Table 1a). The sensitivity evaluation
suggests that the assumption concerning q is reasonable and
will not affect the overall conclusions that we will draw
hereinafter.
1617
Fig. 3. Parameter estimates obtained using consumption data of constant fraction in seal diet (line with solid squares) and proportional
fraction (line without symbols) and obtained with consumption data
excluded (line with solid triangles). For details see Fig. 2.
Sensitivity to consumption data
Because
the estimated number at age consumed by grey
~
seals, C tp, a , depends on the assumption made regarding cod
fraction in the seal diet, it is necessary to explore predation
~
scenarios (constant- and proportional-fraction sets of C tp, a )
and examine how they affect the estimation of other parameters. In addition, we also estimate parameters after excluding
the seal-consumption data to evaluate the performance of
partition of M.
The estimates of Mm, F, and SSB are nearly identical under the three scenarios of seal consumption: (1) assuming a
constant fraction, (2) assuming a proportional fraction, and
(3) excluding the consumption data (Fig. 3). Assuming a
constant fraction results in higher estimates of Mi (except for
the last 2 years) and R. The R estimates from the third scenario (with consumption data excluded) are closer to those
from the second scenario, which assumes a proportional
fraction. Before 1983, when Mp was small, the Mi estimates
from the third scenario are also closer to those from the second scenario. When the consumption data are excluded, the
estimate of Mi rises gradually after 1988, reflecting the increase in Mp. The RSS from the second scenario (proportional fraction) is the lowest, and it increases drastically
when the consumption data are
~ excluded (Table 1b). In the
following analyses, the data C tp, a from the second scenario
are used.
Sensitivity to penalty weighting
The estimates of Mi and Mm are closely related to the
weighting factors l M i and l M m with higher levels resulting in
reduced variations. Simulation studies indicate that appropriate weighting levels are related to measurement error in research-survey data (Fu 2000). We increased l M i and l M m by
a factor of 3 from the originally assigned levels and then reduced them by factors of 3 and 6 to check sensitivity.
When the levels of l M i and l M m increase threefold, the
estimates of Mi and Mm are nearly flat (Fig. 4). Recruitment
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1618
Fig. 4. Parameter estimates obtained using four sets of penalty
weighting factors l M i and l M m : 7500 and 5000 (line without symbols), 3 times larger (broken line), 3 times smaller (line with ×),
and 6 times smaller (line with open squares). For details see Fig. 2.
Can. J. Fish. Aquat. Sci. Vol. 58, 2001
Table 1. Residual sums of squares (RSS) from scenarios of sensitivity evaluation on catchability (a), seal consumption (b), and penalty
weightings of natural mortality variability, l M i and l M m (c).
Catchability
Seal consumption
l M i and l M m
RSS
(a) Catchability
0.3
Constant
0.8
Constant
0.4, 0.6
Constant
7500, 5000
7500, 5000
7500, 5000
165 923
188 198
162 467
(b) Seal consumption
0.4, 0.6
Constant
0.4, 0.6
Fraction
0.4, 0.6
Excluded
7500, 5000
7500, 5000
7500, 5000
162 467
157 010
258 470
(c) Penalty weightings of natural mortality variability, l M i
0.4, 0.6
Fraction
7500, 5000
0.4, 0.6
Fraction
2500, 1600
0.4, 0.6
Fraction
1250, 830
0.4, 0.6
Fraction
22500, 15000
and l M m
162 467
137 419
130 773
185 962
Mi, Mm, and R; however, the overall time trend in the parameter estimates is not changed. Reducing l M i and l M m by a
factor of 6 results in similar estimates of Mi and R, but much
higher Mm, in the last 4 years. The RSS declines when the
weighting factors are reduced (Table 1c), Although lower
levels of the weighting factors are desired under low measurement errors with a resultant better fit to the data (Fu
2000), the uncertainty in the accuracy of the survey data led
us to retain the intermediate levels.
Parameter estimation and standard error
Using catchability q1 and q2 of 0.4 and 0.6, respectively,
the consumption scenario of proportional fraction, and the
originally assigned penalty weighting factors for natural
mortality deviations, we estimated the population parameters. Figure 5 shows the selectivity curves. Standard errors
of the mortality parameters, R, and SSB were obtained from
the bootstrap procedure (Fig. 6). The estimated Mp averaged
over ages 1–4 has increased dramatically since 1988, and is
nearly twice as large as Mi in the terminal year. The estimated Mi has two peaks, one in the early 1970s and another
in the early 1980s, but has remained at a stable level since
the mid-1980s. In contrast, the estimated Mm remains around
0.2 until 1990, after which it increases dramatically. The estimated F is around 0.7 in the 1970s, declines to 0.17 in
1977 at the time of extension of jurisdiction, and remains
around 0.5 throughout the 1980s. Fishing mortality starts to
climb in 1989 and peaks at 1.2 in 1992 before the fishery
closure took place in 1993. The estimated R has one prominent peak in the early 1980s, and declines steadily after
1988. The estimated SSB declines steadily in the 1970s before starting to climb in 1977. SSB peaks in 1985, but declines steadily afterwards. Estimated total mortality from the
model for both immature and mature cod agrees well, in
general, with that directly calculated from the survey data
(Fig. 7). However, survey data give much higher estimates of
Mm for the last 3 years.
estimates decrease correspondingly and the RSS increases
substantially. When the levels of l M i and l M m are reduced
by a factor of 3, there are more dynamics in the estimates of
Retrospective analysis
Compared with previous results based on SPA (Mohn et
al. 1998), retrospective analysis produces a much less severe
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Fu et al.
Fig. 5. Selectivity curves for predation (line with solid squares),
survey gear (line without symbols), and commercial gear from
1970 to 1976 (line with solid triangles), from 1977 to 1982 (line
with ×), and from 1983 to 1997 (line with open squares).
1619
Fig. 6. Parameter estimates obtained using catchability q1 and q2 of
0.4 and 0.6, consumption data of proportional fraction in seal diet,
and penalty weighting factors l M i and l M m of 7500 and 5000. For
details see Fig. 2. Standard errors are shown as bar lines.
retrospective pattern in the estimates of all parameters except Mm (Fig. 8). The shape of the Mm estimates in the
1990s changes dramatically, from increasing to leveling out,
when the last 2 years’ data are removed. In addition, the estimates of Mi and R with data only up to 1984 deviate substantially from the values obtained from the analysis of the
entire historical data series.
Discussion
This paper presents an age-structured model that uses multiple data sources from commercial-fishery, research-survey,
and seal-diet analysis. This is the first stock-assessment study
that estimates annual variations in natural mortality of both
immature and mature cod. Our estimates of mortality indicate
that except for the increase in F from 0.78 in 1991 to 1.2 in
1992, there is no dramatic increase in Mp, Mi, and Mm over
the years 1991 and 1992. Our major conclusion is that the
abrupt decline of the 4VsW cod stock in the early 1990s is
unlikely to have been due to a sudden increase in M, and fishing appears to have been the primary cause.
The estimation of natural mortality indicates that Mi is
more variable than Mm, which remains around 0.2 except in
the last 4 years. Simulation studies indicate that M should be
estimated annually when it varies over time (Fu and Quinn
2000). The variability in the Mi estimates suggests that Mi
should be estimated each year as has been done here. When
consumption data are excluded from the parameterestimation procedure, the estimated Mi increases continuously after 1988, consistent with the increasing trend in the
Mp estimates. This further suggests that estimating Mi annually is important, particularly when consumption data are
unavailable. Estimating annual Mi captures mortality
changes, whether they are due to predation or to other factors. Another major conclusion from this study is that estimates of Mp have increased dramatically since 1988
irrespective of the predation scenario. The consistency between the increasing trend in Mp and the difference between
two series of Mi estimated with and without the consumption
data indicates that partition of immature cod mortality into
Mp and Mi is practical.
Sensitivity examination indicates that the estimate of Mi is
robust to the assumption of q and primarily controlled by the
weighting factor l M i . Smaller measurement errors in survey
data favor smaller weighting. However, if measurement er© 2001 NRC Canada
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1620
Fig. 7. Total mortality (Z) estimated from the model (line) and
solely from the survey data (solid triangles) for both immature
cod (a) and mature cod (b).
Can. J. Fish. Aquat. Sci. Vol. 58, 2001
Fig. 8. Parameter estimates from retrospective analyses using
data from 1970 to 1983 and all the way up to 1997. For details
see Fig. 2.
rors are large and a small value is assigned to l M i , then the
Mi estimates can be overly sensitive to the errors in the survey data. On the other hand, if the measurement errors are
lower than assumed, we run the risk of underestimating the
magnitude and variability of Mi for the three periods of
peaks in Mi: the early 1970s, early 1980s, and 1990s. Nevertheless, such an underestimation would not change our view
of the stock status or our conclusions.
In contrast, the estimate of Mm is closely related to the q
value. The higher q value, the lower the Mm estimates will
be. Nevertheless, the time trend is not changed if the assumption of the overall q level is wrong. The estimates of
Mm are rather stable before the decline of the stock in 1990s;
however, they have increased by a factor of 3 over the last 7
years. It was noted that Mm was the only variable that displayed a severe retrospective pattern. Removing the last 2
years’ data changes the shape of the Mm estimates completely. Further examination of the trend towards an increase
in Mm estimates indicates
that it is primarily caused by the
~
low survey values of N t, a in 1996 and 1997. Replacing these
2 years’ data by those from 1995 gives a much slower increase in the Mm estimates.
Why did the survey estimates of mature cod abundance in
1996 and 1997 drop abruptly? The exact reasons are not
known, but there are at least three possibilities. The first possibility is that the fish moved away and were unavailable to
survey gear, as suggested by Rose et al. (2000) for the cod
stocks off Newfoundland. However, this possibility is slim
for the 4VsW cod stock because there is no evidence that
cod abundance increased in other adjacent areas. The second
possibility is that mature cod simply died, as the high Mm
estimates suggest. Fishermen videotaped numerous carcasses
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Fu et al.
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Fig. 9. (a) Comparisons among portions of immature cod biomass lost as a result of fishing mortality (grey-shaded area), predation
mortality (open area), average immature-cod mortality, Mi (or Mi if it is less than the average) (dotted area), and the portion of Mi beyond its average (hatched area). The area below the broken line represents immature cod biomass that survived each year. (b) Comparisons among portions of mature cod biomass lost as a result of fishing mortality, predation mortality, 0.2 (or Mm if it is less than 0.2),
and the portion of Mm beyond 0.2. The area below the lower broken line represents the mature cod biomass that survived each year,
and that below the higher broken line represents the biomass of age 4 cod that survived each year. In c and d, biomass loss is shown
as a percent for immature and mature cod, respectively.
of large cod left by seals that fed solely on the belly of these
fish off Newfoundland, a form of predation not detectable
by diet-estimation studies. The third possibility is that low
recruitment throughout the early 1990s failed to replenish
the mature cod stock. The low recruitment may have been
due to environmental changes that reduced reproductive
potential (Lambert and Dutil 2000); environmental changes
are evident from the changes in species composition (Frank
et al. 1996) and physical oceanography (Drinkwater and
Mountain 1997). If the last two possible scenarios did occur,
failure of the 4VsW cod stock to recover after the moratorium on commercial fishing would be expected.
Overall, the significant advance in our work is the relaxation of the assumption of a constant M, an assumption that
can be easily violated (Fu 2000; Shelton and Lilly 2000).
The estimation of annual variations in M leads to changes in
the R estimates. Our R estimates are generally larger than
those in Mohn et al. 1998, particularly for the early 1980s.
Natural mortality and recruitment are positively correlated.
When high M and high R values coexist, assessment models
that assume a low constant M, such as 0.2, would underestimate the corresponding R. Thus, Mohn et al. (1998) appear
to have systematically underestimated R. The extremely high
R estimates from our model for the early 1980s are consistent with the research surveys that also reveal an extremely
high R value in the early 1980s (Mohn et al. 1998). Overall,
R estimates from assessment models of constant M could
largely deviate from the true values if M, in fact, varies over
time. Estimating annual variations in M is essential to a
better understanding of the underlying population dynamics.
After the cod stocks off southern Labrador and eastern
Newfoundland collapsed suddenly in 1992, it was hypothesized that M increased in 1991 (Myers and Cadigan 1995).
A precipitate loss of 700 million fish was estimated for cod
older than age 2 in 1991, corresponding to an average M
value of 1.14 compared with the level of 0.2 assumed in
cod-stock assessments (Shelton and Lilly 2000). However,
the hypothesis of a sudden increase in M in 1991 was rejected (Hutchings and Myers 1994; Myers and Cadigan
1995), and fishing mortality was regarded as sufficient cause
for the collapse of the stock (Myers et al. 1996; Walters and
Maguire 1996). Our estimates of mortalities F, Mp, Mi, and
Mm before 1993 support the finding in Myers and Cadigan
(1995). In particular, when the data up to 1995 are used
(leaving out the data from 1996 and 1997), the estimated Mm
in the early 1990s declines slightly.
Could a precipitate drop in cod biomass similar to that of
the cod stocks off southern Labrador and eastern Newfoundland (Shelton and Lilly 2000) also have happened to the
4VsW cod stock? We take advantage of the estimates of annual variations in mortality and recruitment to explore population dynamics through the entire observation history. To
reveal biomass loss due to various mortalities, we partitioned
the total biomass loss of mature cod into four parts: loss due
to F, Mp, 0.2 (or Mm if it is less than 0.2), and the portion of
Mm beyond 0.2. Although the cod fishery in 4VsW appears
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1622
to have collapsed over 1991 and 1992, the decline in survival of mature cod has taken place since 1985 (Fig. 9).
Since 1988, the quantity of fish that died has been greater
than that which survived. In 1992, the percent of mature cod
that died reached a peak. Replenishment from age 4 cod has
been low since 1985, except for the increases in 1990 and
1991, corresponding to the relatively high R estimates in
1987 and 1988. However, the abundance of surviving age 4
cod dropped dramatically in 1992 despite the fact that Mi
and Mm remained at historically low levels. Off southern
Labrador and eastern Newfoundland, young cod aged 4 and
5 in 1990 and 1991 resulting from high recruits in 1986 and
1987 were similarly predominant in the catches made just
before the fishery closure, which was attributed to the relative absence of older fish (Myers et al. 1996). With Mm remaining around the historical average level of 0.2, it can be
concluded that a high F value and insufficient recruitment of
age 4 cod to the mature cod stock have contributed to the
continuous decline in mature cod biomass.
To envisage the biomass dynamics of immature cod, we
also partitioned the total biomass loss into four parts: loss
due to F, Mp, average of the Mi estimates (or Mi if it is below
the average), and the portion of Mi beyond its average. Before the fishery collapse, there were two periods when loss
of immature cod biomass exceeded 50%, one in the early
1970s and another in the early 1980s. The large loss of immature cod biomass in the early 1980s may have contributed
to the reduction in recruitment of age 4 cod to the mature
cod stock. The causes of the large biomass loss are
unknown, but it is consistent with the widely discussed period
of extensive discarding of undersized fish (Mohn et al. 1998).
Overall, we conclude that fishing mortality may have been the
primary cause of the collapse of the 4VsW cod stock.
It was suggested that the unbridled increase in F just before the collapse was caused by overestimation of stock size
(Walters and Maguire 1996), statistical bias inherent in the
estimation procedures (Myers et al. 1996), or increased concentration of cod at low stock size (Hutchings and Myers
1994; Hutchings 1996; Rose et al. 2000). Based on their statistical analysis, Myers et al. (1995) suggested that the cod
stocks would recover after the moratorium on fishing. However, this has not happened up to this point, 10 years after
the moratorium. Why are the stocks not recovering? What
happened to the cod stocks after the collapse? Our Mp, Mi,
and Mm estimates for the 4VsW cod stock after its collapse
demonstrate that Mp became an important factor affecting
the survival of immature cod in the 1990s. Throughout the
1990s, the proportion of immature cod that died was greater
than that which survived. Mature cod may also have been
subject to high natural mortality since the mid-1990s. Recruitment was low in the 1990s. These three factors have
contributed to the failure of the stock to recover.
Acknowledgements
This paper is the result of research sponsored by the
Department of Fisheries and Oceans’ Strategic Research
Project entitled Comparative Dynamics of Exploited Ecosystems in the Northwest Atlantic. We thank Mr. Jerry Black
and Drs. Alida Bundy and Ken Frank (Bedford Institute of
Oceanography, Dartmouth, N.S.) for their help and com-
Can. J. Fish. Aquat. Sci. Vol. 58, 2001
ments. We are especially grateful to Dr. Mike Hammill
(Institut Maurice-Lamontagne, Mont-Joli, Que.) and an
anonymous reviewer whose critical reviews are essential to
the success of this work.
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